A Globally Convergent Algorithm for Neural Network Parameter Optimization Based on Difference-of-Convex Functions
This provides a more reliable optimization method for neural network training, though it is incremental as it builds on existing DC and BCD techniques.
The paper tackles the problem of optimizing parameters for single hidden layer neural networks by proposing a globally convergent algorithm based on difference-of-convex functions and block coordinate descent, achieving linear or faster convergence rates under certain conditions and showing competitive performance against state-of-the-art gradient-based solvers in training and test loss.
We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose a block coordinate descent (BCD) approach that we combine with a tailored difference-of-convex functions algorithm (DCA). We prove global convergence of the proposed algorithm. Furthermore, we mathematically analyze the convergence rate of parameters and the convergence rate in value (i.e., the training loss). We give conditions under which our algorithm converges linearly or even faster depending on the local shape of the loss function. We confirm our theoretical derivations numerically and compare our algorithm against state-of-the-art gradient-based solvers in terms of both training loss and test loss.